All UV info is collapsed into a single point
It's quite common to have 2 UV maps (or UV channels) on the same object, one for the texture maps (the one you show in your question is for the color map), and one for the lightmap.

When importing the model into UE, check the box "Generate Lightmap UV" and UE will create this second UV for you.

If you want to have more control on this map, you can create it manually into Blender :


In Object Data/UVMaps, hit the + button to create a New UVMap, and name it something like "Lightmap UV".
Make sure it is selected, then do your unwrapping as usual. Make sure no face is overlapping another, it's really important for a lightmap. The "Lightmap Pack" unwrap method give nice results (feel free to bump up the "Margin" parameter, it's quite low by default).
Import your model without checking "Generate Lightmap UV". Then refer to UE documentation to assign the correct UV channel to the lightmap : https://docs.unrealengine.com/en-US/Engine/Content/Types/StaticMeshes/LightmapUnwrapping/index.html